Similar to query expansion in ad hoc search [1]}, it is difficult, or often impossible, to directly optimize Equation REF . The document search system, which is used to estimate \(\text{Accuracy}(Q_i \cup \mathcal {S})\) , is in general not differentiable. Thus, many approaches have been developed to obtain \(\mathcal {S}^*\)  approximately using either heuristics or machine learning methods.
